11x11 Queens Puzzle #54
Difficulty: easy. Place 11 queens on this 11x11 board so that no two share a row, column or color region and none touch — including diagonally. This puzzle has exactly one solution, and it has been verified solvable by deduction alone: the complete 18-step reasoning is written out below.
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Step-by-step solution for puzzle #54
What follows is a complete solve of puzzle #54, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 11 queen placements and 7 elimination steps that narrow the board between them. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the pairing argument on rows.
Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on rows, last square in a row.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 2, column 11 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 11, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The khaki region is down to one open square, at row 8, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 1, the remaining khaki squares, and the ring of neighbours around row 8, column 1.
Step 3. Only row 9, column 4 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 4, in orange and in the ring around that square is now dead.
Step 4. Wherever indigo ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 3 of 11 queens placed. Step 5. Mint cannot leave column 10 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 6 squares in all.
Step 6. The slate region has 4 squares left, spread across rows 5–7, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 7. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. All of the teal region's remaining squares (2 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 7 squares come off.
The board after step 8 — 3 of 11 queens placed. Step 9. Only row 10, column 2 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 2, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 10. All of the red region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 11. Slate, red, and pale yellow are now boxed into rows 5–7 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 2 squares at once.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 10; indigo has one square left, so its queen takes row 1, column 8; teal has one square left, so its queen takes row 11, column 9; row 5 is down to one square, putting a queen on row 5, column 6; pale yellow has one square left, so its queen takes row 7, column 7; blue has one square left, so its queen takes row 3, column 5; red has one square left, so its queen takes row 6, column 3. After each one, clear that row, that column, the rest of the colour and the ring of neighbours before looking for the next. The last of them seats the queen on row 6, column 3.
The board after step 12 — 11 of 11 queens placed.
That completes the board: 11 queens seated, one in every row, one in every column and one in every colour, with no two of them touching. Notice that nothing in the sequence above required a guess — each placement followed from an elimination already on the grid, which is what “single solution, solvable by logic” actually means in practice.
About 11x11 Queens puzzle #54
Board #54 of the 11x11 bank carries a easy rating. Its 121 squares are shared between eleven colored regions, and the solution places eleven queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #54 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #54 are: amber (1 square), khaki (1 square), orange (1 square), indigo (4 squares), slate (4 squares), red (8 squares), mint (11 squares), teal (11 squares), sea green (13 squares), pale yellow (32 squares), blue (35 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the blue region is the roomiest area on the grid with 35 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 1 place to put its queen; blue has 35. The spread between them on this board is 34 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Amber is the tidiest shape on #54, packing 100% of its 1×1 bounding box, whereas teal straggles across its 5×4 box at just 55%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #54, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Amber: 1 square across rows 2–2, columns 11–11. It never leaves row 2, so its queen is locked to that row.
Khaki covers 1 square, spanning 1 row and 1 column (rows 8–8, columns 1–1). It never leaves row 8, so its queen is locked to that row.
Orange occupies 1 square within rows 9–9, columns 4–4. It never leaves row 9, so its queen is locked to that row.
Indigo: 4 squares across rows 1–3, columns 8–9.
Slate covers 4 squares, spanning 3 rows and 2 columns (rows 5–7, columns 5–6).
Red occupies 8 squares within rows 5–7, columns 2–5.
Mint: 11 squares across rows 1–6, columns 9–11.
Teal covers 11 squares, spanning 5 rows and 4 columns (rows 7–11, columns 8–11).
Sea green occupies 13 squares within rows 8–11, columns 1–4.
Pale yellow: 32 squares across rows 4–11, columns 4–10.
Blue covers 35 squares, spanning 7 rows and 8 columns (rows 1–7, columns 1–8).
Where to start on this board
Begin where the choices are fewest. On this board that means amber, which owns just 1 square inside a 1×1 window running from row 2 to row 2 and column 11 to column 11. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. Then look at which colors just lost ground: on a grid this size that one observation usually forces a second region within a move or two.
Work outward to the other flat regions next. Khaki and orange are no more than two rows tall, so their queens are confined to a narrow band. When two flat regions overlap the same pair of rows, those rows are spoken for and every other color is locked out of both — the single most productive pattern in the game, and it is live on this board.
The tightest lines on puzzle #54
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 4, 10 and 11 are the narrowest, touched by only 3 colors. Column 7 is the tightest column, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 7, meeting 5 colors, is the opposite case — the busiest line on #54 and the last one you should expect to crack.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
Keep alternating between two views of the board. In the region view you ask which of the eleven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 11x11 board unwinds.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #54 is rated easy
The rating reflects how much the board concedes up front. Puzzle #54 has six regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 34 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
Techniques that work well at 11x11
At 11x11 you are managing 121 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #54 the place to look for one is around column 7.
Here is a shape check that gives nothing away: when #54 is solved, 4 queens sit on the outer edge of the grid and 7 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
How to play Queens
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- Tap once to mark a square with an X (where a queen can't go), tap again to place a queen, and once more to clear it.
- There is always exactly one valid solution. Use logic, never guessing, to find it.
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Questions about this puzzle
How hard is 11x11 Queens puzzle #54?
Puzzle #54 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and six of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #54 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #54, has been verified to have exactly one valid arrangement of eleven queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #54?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.